Re: simplifying square root basic one

Hi bronxsystem,

Edit: I'm not sure if I should have posted this because I don't know the proper method (I've forgotten more than I learnt!), and there's probably a better (or 'book') way to do it. My approach seems to work for these two problems, and so it may help in some way.

I would look at the first problem like this...

- Find the largest perfect square in 32: ie, 16 - Place its square root (4) in front of the square root sign - The remaining radicand is 2 (from 32/16 = 2).

The solution for the second problem is identical to that for the first: - Find the largest perfect square in b³: ie, b² - Place its square root (b) in front of the square root sign - The remaining radicand is b (from b³/b² = b³⁻² = b¹ = b)

This next bit is just some additional info that may help with understanding what's going on, but is nothing to do with solving the problems:The reverse process (ie, to 'unsimplify' the solutions and to revert to the original problems) would be to: - square the number that is outside the sign (4) to become 16 (or b² for the variable), and - multiply the result by the radicand to form a new radicand value (ie, 32, or b³).

Last edited by phrontister (2014-01-16 20:10:24)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Re: simplifying square root basic one

Re: simplifying square root basic one

Thanks for that, bronxsystem.

Looks like I was close, the main difference being my non-technical wording (which I've now improved in my post) and that I referred to finding the largest perfect square (which I think is correct because simplification is to the lowest form, not an intermediate one...which a lower perfect square - if it exists - would give).

Re the wording of the following:

To summarize, then, a radical can be simplified if the following statements are true:

I would have written that as:

To summarize, then, a radical can be simplified if one or more of the following statements are true:

...for obvious reasons.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson